On multiplier systems and theta functions of half-integral weight for the Hilbert modular group $\mathrm{SL}_2(\mathfrak{o})$

Hiroshi Noguchi

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arXiv · 2102.10723

On multiplier systems and theta functions of half-integral weight for the Hilbert modular group $\mathrm{SL}_2(\mathfrak{o})$

Hiroshi Noguchi

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Abstract

Let $F$ be a totally real number field and $\mathfrak{o}$ the ring of integers of $F$. We study theta functions which are Hilbert modular forms of half-integral weight for the Hilbert modular group $\mathrm{SL}_2(\mathfrak{o})$. We obtain an equivalent condition that there exists a multiplier system of half-integral weight for $\mathrm{SL}_2(\mathfrak{o})$. We determine the condition of $F$ that there exists a theta function which is a Hilbert modular form of half-integral weight for $\mathrm{SL}_2(\mathfrak{o})$. The theta function is defined by a sum on a fractional ideal $\mathfrak{a}$ of $F$.

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Hiroshi Noguchi. 2021-02-22. On multiplier systems and theta functions of half-integral weight for the Hilbert modular group $\mathrm{SL}_2(\mathfrak{o})$. https://arxiv.org/abs/2102.10723

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